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On the accuracy of the calculation of transient growth in plane Poiseuille flow
Author(s) -
Zhao Shi,
Duncan Stephen
Publication year - 2014
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3875
Subject(s) - hagen–poiseuille equation , galerkin method , discretization , mathematics , spurious relationship , spectral method , numerical analysis , basis function , flow (mathematics) , plane (geometry) , eigenvalues and eigenvectors , mathematical analysis , collocation (remote sensing) , transient (computer programming) , geometry , finite element method , physics , computer science , operating system , statistics , quantum mechanics , machine learning , thermodynamics
SUMMARY This paper addresses the accuracy of numerical methods to compute the transient energy growth of plane Poiseuille flow. We show that using the Chebyshev collocation method to discretize the linearized governing equations in the wall‐normal direction can introduce numerical problems when computing the energy evolution of the flow. We demonstrate that spurious eigenmodes of the discretized linear operator and numerical integration errors are the possible sources of the numerical problems, and we also show that spurious eigenvalues with negative real parts of large magnitude can affect the calculation of energy growth. These difficulties can be avoided by using a spectral Galerkin method where the basis functions satisfy the boundary conditions. Copyright © 2014 John Wiley & Sons, Ltd.